Radiative B meson decay through the b → sγ process has been one of the most sensitive probe of new physics beyond the Standard Model, because of its importance in understanding the phenomenon of CP violation, which is believed to be necessary to explain the excess of matter over anti-matter in our universe. The inclusive picture of the b → sγ process is well established; however, our knowledge of the exclusive final states in radiative B meson decays is rather limited. We have investigated one of them, the exclusive, radiative B decay to the charmless K*2 (1430) meson, in a sample of 88.5 × 106 BB¯ events with the BABAR detector at the PEP-II storage ring. We present a measurement of the branching fractions B (B0 → K*2 (1430)0γ) = (1.22 ± 0.25 ± 0.10) × 10−5 and B (B+ → K*2 (1430)+γ) = (1.45 ± 0.40 ± 0.15) × 10−5, where the first error is statistical and the second systematic. In addition, we have performed the first search for direct CP violation in this decay with the measured asymmetry in B0 → K*2 (1430)0γ of ACP = −0.08 ± 0.15 ± 0.01.^